COMPUTERSIMULATION OF COMPLEX

1. COMPUTERSIMULATION OF COMPLEX (BIO-)MOLECULAR SYSTEMS Possibilities, Impossibilities and Perspectives

2. Thales 600 B.C. observe model design experiment Galileo 1500 A.D. model observe model mimic reality on a computer Rahman 1980 A.D. model observe model Computersimulation of reality real world experiment experimentaldata classificationabstractionsimplificationapproximationgeneralisation comparingistesting modelof the world computationalmethods predictions Three important turns in science:

3. Computersimulation of biomolecular systems • 1) Why • 2) How • What • 4) And the future … do we simulate ?

4. Computersimulation of biomolecular systems • 1) Why • 2) How • 3) What • 4) And the future … do we simulate ?

5. For which problems are simulations useful ? • Simulation can replace or complement the experiment: • Experiment is impossibleInside of starsWeather forecast • Experiment is too dangerous Flight simulationExplosion simulation • Experiment is expensive High pressure simulation • Windchannel simulation • Experiment is blind Some properties cannot be observed on very short time- scales and very small space- scales

6. For which problems are simulations useful ? Simulations can complement the experiment: Simulation explains experiments Properties of water Folding of protein molecules Simulation suggests Design of drugs new experiments enzymes knowledge new ideas less experiments better chance of success

7. The world of molecular simulation and experiment experiment simulation Resolution* size :1023 molecules 1 molecule time : 1 second 10-15 seconds *: Single molecules / 10-15 seconds possible (but not both in the liquid phase) (restricted) (unrestricted) Typical space / time scales size : 10-3 meter 10-9 meter time : 103 seconds 10-6 seconds Simulation and experiment are complementing methodsto study different aspects of nature

8. Computersimulation of biomolecular systems • 1) Why • 2) How • 3) What • 4) And the future … do we simulate ?

9. Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly bound to each other Degrees of freedom: atoms are the elementary particles Forces or interactions between atoms Boundary conditions MOLECULAR MODEL system temperature pressure Force Field =physico-chemicalknowledge Methods to generate configurations of atoms: Newton

10. Choose relevant degrees of freedom: elementary particles Restricted applicability More model parameters Empirical parameters Less expensive Broader applicability Less model parameters Physical parameters More expensive . . . . . . = Particles: all atoms (excluding solvent) classical mechanics Force Field (including solvent) all atoms classical mechanics Force Field (atomistic) monomers classical mechanics Force Field (statistic) atomic nuclei + electrons quantummechanics electrostatics Description: Interactions:

11. Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly attached Degrees of freedom: atoms are the elementary particles Forces or interactions between atoms Boundary conditions MOLECULAR MODEL system temperature pressure Force Field =physico-chemicalknowledge Methods to generate configurations of atoms: Newton

12. non-bonded interactions bonded interactions Bond stretching Angle bending - - - + Electrostatic interactions Rotation around bond Planar atomgroups van der Waals interactions Interactions in atomic simulaties : Force Fieldphysico-chemical knowledge

13. Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly attached Degrees of freedom: atoms are the elementary particles Forces or interactions between atoms Boundary conditions MOLECULAR MODEL system temperature pressure Force Field =physico-chemicalknowledge Methods to generate configurations of atoms: Newton

14. Determinism … Classical dynamics Situation at time t Force is determined by relative positions acceleration = force / mass velocity = acceleration × t position = velocity× t position velocity force Situation at time t+t Sir Isaac Newton 1642 -1727

15. Generating configurations in atomic simulations: molecular dynamics ... comparable to shooting a movie of a molecular system... velocities Time t positions forces Time (t+t) new velocities new positions t  10-15 seconds

16. Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly attached Degrees of freedom: atoms are the elementary particles Forces or interactions between atoms Boundary conditions MOLECULAR MODEL system temperature pressure Force Field =physico-chemicalknowledge Methods to generate configurations of atoms: Newton

17. Boundary conditions in atomic simulations Vacuum • Surface effects (surface tension) • No dielectric screening • Still surface effects • Only partial dielectric screening • Evaporation of the solvent Advantage: • No surface effectsDisadvantage: • Artificial periodicity • High effective concentration Probably still the best approach… Droplets Periodic: rectangular system is surrounded by copies of itself

18. Computersimulation of biomolecular systems • 1) Why • 2) How • 3) What • 4) And the future… in my research group Methods Applications do we simulate ?

19. What do biochemists or molecular biologistswant to know of molecules? • stable structures binding equilibrium energetically favourable structures between two small organic molecules • Relation between structure and function water transport in the enzymes binding cavity of aprotein (FABP) • Motions en mechanisms prediction of the three-  protein folding dimensional structure orthe folding of proteins (polypeptides) • Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor

20. Applications of molecular dynamics simulation: Example 1 Structural interpretation ofthermodynamic properties: Binding equilibrium between two small organic molecules

21. HO HO Binding equilibrium Complex : Hydrogen bonds H Cyclohexane- diamine Cyclopentane- diol H ? N - NH2 H + O H NH2 H N H + Many different bindingmodes O - Average binding strength (free enthalpy) : Experimental MD simulation BenzeneCCl4 Gb [kJ/mol] -9.3 -11.5 -10.4

22. Diol + Diamine + 252 CCl4 Molecules 2.1 – 2.2.10-9 seconds Complex formed Formation of the complex (camera focuses on the diamine)

23. Diol + Diamine + 252 CCl4 Molecules 3.2 – 4.0.10-9 seconds Hydrogen bonds O  N N  O … and a nanosecond later … the molecules are free again…

24. NH2 NH2 NH2 NH2 NH2 NH2 HO HO HO HO HO HO NH2 NH2 NH2 NH2 NH2 NH2 HO HO HO HO HO HO Results of the simulation (over 10-7 sec) :  Experimentally hardly (or not) possible ! Occurrence of different binding modes : 54% 21% 8% 7% 4% 3% Life time : • Average life time of the complex: 2.10-10 sec (max. 3.10-9 sec) • Average life time of a hydrogen bond: 5 .10-12 sec

25. What do biochemists or molecular biologistswant to know of molecules? • stable structures binding equilibrium energetically favourable structures between two small organic molecules • Relation between structure and function water transport in the enzymes binding cavity of aprotein (FABP) • Motions en mechanisms prediction of the three-  protein folding dimensional structure orthe folding of proteins (polypeptides) • Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor

26. Carbohydrates: storage of energy and molecularstamps Biomolecules Boundaries: membranes consist of lipidswith pores of proteins Proteins: e.g. haemoglobin for oxygen transport Hereditary information in the nucleus: DNA

27. Applications of molecular dynamics simulation: Example 2 The watertransport in the binding cavity of a protein (FABP) • Important to understand enzymatic reactions: the dynamics of the binding cavity • Simulation allows one to follow the movements of individual molecules

28. What do biochemists or molecular biologistswant to know of molecules? • stable structures binding equilibrium energetically favourable structures between two small organic molecules • Relation between structure and function water transport in the enzymes binding cavity of aprotein (FABP) • Motions en mechanisms prediction of the three-  protein folding dimensional structure orthe folding of proteins (polypeptides) • Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor

29. Proteins consist of chains of amino acids (primary structure) Applications of molecular dynamics simulation: Example 3 Protein folding the challenge 20 kinds In an organism proteins only function if they have been correctly folded three- dimensionally. (secondary and tertiary structure) • What is the relation between amino acid sequence and folded spatial structure? • How does the folding process take place?

30. Foldingsimulation • Proteins are too large systems to simulate the slow folding process. • Smaller model compounds can be correctly folded on the computer. • Information about folding mechanisms and the unfolded state: surprise

31. all different? how different? 321 1010 possibilities!! Unfolded structures Folded structures all the same

32. Surprising result after simulations of many polypeptides The number of relevant unfolded structures is much and much smaller than the number of possible unfolded structures number of number of amino acids in the protein 10 100 Folding time (exp/sim) in seconds 10-8 10-2 possible structures 320 109 3200 1090 relevant (observed) structures 103 109 peptide protein • Assuming that the number of relevant unfolded structures is proportional to the folding time, only 109 protein structures need to be simulated instead of 1090 structures. • Folding mechanism is simpler than generally expected: searching through only 109 structures • Protein folding on a computer is possible before 2010

33. For which problems are simulations useful ? Simulations can complement the experiment: Simulation explains experiments Properties of water Folding of protein molecules Simulation suggests Design of drugs new experiments enzymes knowledge new ideas less experiments better chance of success

34. What do biochemists or molecular biologistswant to know of molecules? • stable structures binding equilibrium energetically favourable structures between two small organic molecules • Relation between structure and function water transport in the enzymes binding cavity of aprotein (FABP) • Motions en mechanisms prediction of the three-  protein folding dimensional structure orthe folding of proteins (polypeptides) • Design of new compounds binding strength of design of drugs hormone replacing molecules to the estrogenreceptor

35. a “new key”?: The active site with the molecule to be tested the “key hole”: the active site in the protein containing a “fitting key”: the active site with an active molecule the active and a new molecule (to be tested) superimposed Applications of molecular dynamics simulations: Example 4 Design of drugs testing compounds with the computer Enzymes work according to the “lock and key”-principle

36. Polychlorinated biphenyls Unphysical reference state 16 hydroxylated PCB’s

37. Binding to the estrogen receptor 16 hydroxylated PCB’s: 10 < kBT  2.5 kJ mol-1 13 < 1 kcal mol-1 Average deviation: 2.5 kJ mol-1 Variation exp. values: 4.2 kJ mol-1

38. Computersimulation of biomolecular systems 1) Why 2) How 3) What 4) And the future …

39. History: classical molecular dynamics simulations of biomolecular systems Year molecular system: type, size length of the simulation in seconds 1957first molecular dynamics simulation (hard discs, two dimensions) 1964atomic liquid (argon) 10-11 1971molecular liquid (water) 5 .10-12 1976protein (no solvent) 2 .10-11 1983protein in water 2 .10-11 1989 protein-DNA complex in water 10-10 1997polypeptide folding in solvent 10-7 2001micelle formation 10-7 200xfolding of a small protein 10-3

40. But : • Upper limit to computer speed ? • Accuracy of classical models and force fields ? • Better approximations and simplifications And the future ... Computer speed increases with a factor 10 about every 5½ year! Standard classical simulations : • 2001Biomolecules in water (~104 atomen) 10-8 sec • 2029Biomolecules in water 10-3 sec • 2034E-coli bacteria (~1011 atoms) 10-9 sec • 2056Mammalian cell (~1015 atoms) 10-9 sec • 2080Biomolecules in water 106 sec • 2172Human body (~1027 atoms) 1 sec Protein folding sooner? As fast as nature !

41. Computersimulation of reality real world experiment experimentaldata classificationabstractionsimplificationapproximationgeneralisation comparingistesting modelof the world computationalmethods predictions

42. Acknowledgements • Gruppe informatikgestützte Chemie (igc) http://www.igc.ethz.ch • Dirk Bakowies (Germany) • Riccardo Baron (Italy) • Indira Chandrasekhar (India) • MarkusChristen (Switzerland) • PeterGee (England) • Daan Geerke (Holland) • Daniela Kalbermatter (Switzerland) • Alice Glättli (Switzerland) • David Kony (France) • ChrisOostenbrink (Holland) • Daniel Trzesniak (Brasil) • Alex de Vries (Holland) • HaiboYu (China)